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Simplifying 16r2 + -8r + -1 = 0 Reorder the terms: -1 + -8r + 16r2 = 0 Solving -1 + -8r + 16r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.0625 + -0.5r + r2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + -0.5r + 0.0625 + r2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + -0.5r + r2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + -0.5r + r2 = 0 + 0.0625 -0.5r + r2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 -0.5r + r2 = 0.0625 The r term is -0.5r. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5r + 0.0625 + r2 = 0.0625 + 0.0625 Reorder the terms: 0.0625 + -0.5r + r2 = 0.0625 + 0.0625 Combine like terms: 0.0625 + 0.0625 = 0.125 0.0625 + -0.5r + r2 = 0.125 Factor a perfect square on the left side: (r + -0.25)(r + -0.25) = 0.125 Calculate the square root of the right side: 0.353553391 Break this problem into two subproblems by setting (r + -0.25) equal to 0.353553391 and -0.353553391.Subproblem 1
r + -0.25 = 0.353553391 Simplifying r + -0.25 = 0.353553391 Reorder the terms: -0.25 + r = 0.353553391 Solving -0.25 + r = 0.353553391 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + r = 0.353553391 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + r = 0.353553391 + 0.25 r = 0.353553391 + 0.25 Combine like terms: 0.353553391 + 0.25 = 0.603553391 r = 0.603553391 Simplifying r = 0.603553391Subproblem 2
r + -0.25 = -0.353553391 Simplifying r + -0.25 = -0.353553391 Reorder the terms: -0.25 + r = -0.353553391 Solving -0.25 + r = -0.353553391 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + r = -0.353553391 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + r = -0.353553391 + 0.25 r = -0.353553391 + 0.25 Combine like terms: -0.353553391 + 0.25 = -0.103553391 r = -0.103553391 Simplifying r = -0.103553391Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.603553391, -0.103553391}
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